Answers
The measure of x = 64°
Vertical opposite angles:The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal.
Here we have
Three lines are intersected and formed a triangle
Let's assume that the triangle formed is ΔABC
In ΔABC, ∠C = 34°
Since Vertical opposite angles are equal
=> ∠B = 30°
As we know the sum of angles in a triangle = 180°
=> ∠A + ∠B + ∠C = 180°
=> ∠A = 180° - 30° - 34°
=> ∠A = 116
From the line CL [ observe the given picture ]
=> ∠A + x = 180°
=> 116° + x = 180°
=> x = 180° - 116°
=> x = 64°
Therefore,
The measure of x = 64°
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Related Questions
Find the 15th term in the geometric sequence 20,10,5,2.5
Answers
The 15th term of the given geometric sequence will be (C) 5/4096.
What is a geometric sequence?Mathematicians refer to a succession of non-zero numbers as a geometric progression or geometric sequence.
Each term after the first is derived by multiplying the previous term by a fixed, non-zero value called the common ratio.
So, the geometric sequence will be:
nth term formula: aₙ = a₁rⁿ⁻¹
Now, insert the values and calculate as follows:
aₙ = a₁rⁿ⁻¹
a₁₅ = 20(1/2)¹⁵⁻¹
a₁₅ = 20(1/2)¹⁴
a₁₅ = 20(1/16384)
a₁₅ = 20/16384
a₁₅ = 5/4096
Therefore, the 15th term of the given geometric sequence will be (C) 5/4096.
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Complete question:
Find the 15th term in the geometric sequence below. 20, 10, 5, 2.5, . . .
A.-25/4,096
B.-5/4,096
C.5/4,096
D.25/4,096
4. What is the area of the triangle shown on the graph below?
(1) 10
(2) 11
(3) 14
(4) 25
Answers
Answer:
Step-by-step explanation:
The area of each triangle is one-half the area of the rectangle. So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.
PLEASE HELPPP ASAP I REALLY NEED MATH HELPPPP
Answers
The graph of the odd-degree polynomial reaches positive and negative infinity.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
The given polynomial is shifted towards the left it reaches negative infinity quicker than positive infinity.
Also, the graph of the polynomial is of odd degree as it is symmetric about the origin shifted towards left.
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When writing 2–√5
2
5
as 2n
2
n
, which statement is true about the value of n
n
?
Responses
The value of n
n
is 15
1
5
because (2–√5)5=21
(
2
5
)
5
=
2
1
and (21/5)5=21
(
2
1
/
5
)
5
=
2
1
, so 2–√5=21/5
2
5
=
2
1
/
5
.
The value of n is 1 5 because ( 2 5 ) 5 = 2 1 and ( 2 1 / 5 ) 5 = 2 1 , so 2 5 = 2 1 / 5 .
The value of n
n
is 15
1
5
because (2–√5)5=21
(
2
5
)
5
=
2
1
and (21/5)5=20
(
2
1
/
5
)
5
=
2
0
, so 2–√5=21/5
2
5
=
2
1
/
5
.
The value of n is 1 5 because ( 2 5 ) 5 = 2 1 and ( 2 1 / 5 ) 5 = 2 0 , so 2 5 = 2 1 / 5 .
The value of n
n
is −5
−
5
because (2–√5)5=21
(
2
5
)
5
=
2
1
and (2−5)5=21
(
2
−
5
)
5
=
2
1
, so 2–√5=2−5
2
5
=
2
−
5
.
The value of n is − − 5 because ( 2 5 ) 5 = 2 1 and ( 2 − − 5 ) 5 = 2 1 , so 2 5 = 2 − − 5 .
The value of n
n
is −5
−
5
because (2–√5)5=21
(
2
5
)
5
=
2
1
and (2−5)5=20
(
2
−
5
)
5
=
2
0
, so 2–√5=2−5
2
5
=
2
−
5
.
The value of n is − − 5 because ( 2 5 ) 5 = 2 1 and ( 2 − − 5 ) 5 = 2 0 , so 2 5 = 2 − − 5 .
Answers
The true statement about n is (a) The value of n is 1/5 because (⁵√2)⁵ = 2¹ and (2¹/⁵)⁵ = 1, so ⁵√2 = 2¹/⁵
How to determine the true statement about n?From the question, we have the following parameters that can be used in our computation:
Expression = ⁵√2
Also from the question, we understand that the expression is to be expressed as
2ⁿ
This means that
⁵√2 = 2ⁿ
Re-express ⁵√2 using the law of indices
2ⁿ = 2¹/⁵
By comparison, we have
n = 1/5
This means that the value of n is 1/5
Hence, the true statement is (a)
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Answer:
1236
Step-by-step explanation:
Principal: $225, Interest Rate: 6%, Time: 2 years.
What is simple interest? I know it is something related to PxRxT or something like that.
Answers
Answer:
$27
Step-by-step explanation:
Simple interest is a way of calculating the interest charge on a loan or investment. It is calculated by multiplying the principal amount by the interest rate and the time period. In your example, the simple interest calculation would be $225 * 6% * 2 years = $27.
Answer:
Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that has been earned on the principal. To calculate simple interest, you multiply the principal amount by the interest rate and the length of time the interest is being applied. For example, if you have a principal of $225, an interest rate of 6%, and a time of 2 years, the simple interest would be calculated as follows:
$225 x 6% x 2 years = $27.
In this case, the simple interest on the $225 principal would be $27. This means that after 2 years, you would owe $252 in total, including the original principal and the interest that has been earned on it. Simple interest is typically used for short-term loans or investments, where the interest is paid or earned at regular intervals, such as monthly or annually.
Given the value: 47.728
a. Write the word name of the value.
b. Write the expanded form of the value
c. Use a number line to round this value to the nearest hundredth.
Answers
Your knowledge of the percentage 47.728 is already complete.4772.8% is the percentage equivalent of 47 7 2 8.
What is 47.728 as a Percent?To compute 47.728 as a percentage of a given number x, divide 47.728 by x and multiply the result by 100.
For instance, the ratio of 47.728 to 10 is equal to (47.728 / 10) times 100%, or 477.28%.
Use the decimals to percents converter found below at your convenience.
Place your value in the "% of" area after entering 47.728 in the number field.
Press reset first if you want to restart.
At this point, an automatic conversion to 47.728 in percent will take place.
The answer has been rounded to ten decimal places, as you can see.
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Use the image to answer the question.
What is the surface area of the figure in square centimeters?
Enter your answer as a number, like this: 42
Answers
Answer:
66 [tex]cm^{2}[/tex]
Step-by-step explanation:
Front: 6 x 5 = 30
Back: 6 x 4 = 24
Left side: 1/2 (3 x 4) =6
Right side: 1/2 ( 3 x 4) 6
Add
30 + 24 + 6 + 6 = 66
This season, the probability that the Yankees will win a game a is 0.53 and the
probability that the Yankees will
score 5 or more runs in a game is 0.48. The
probability that the Yankees win and score
and score 5 or more runs is 0.42. What is the
probability that the Yankees will lose when they score 5 or more runs? Round
your answer to the nearest thousandth.
Answers
The probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.
What is Conditional Probability?
Conditional probability, or P(A/B), denotes the likelihood of event A that is dependent on event B.The chance of an event occurring given that another event has already occurred (via assumption, supposition, assertion, or evidence) is known as conditional probability in the field of probability theory.This particular approach assumes that event B occurs in some way related to event A. A conditional probability analysis with respect to event B in this scenario can be performed.The conditional probability formula is given as, [tex]P(M/N)=\frac{P(M\cap N)}{P(N)}[/tex]From the question, we know that the probability that the Yankees will win a game is 0.53.
[tex]\implies P(W)=0.53[/tex]
Also, then the probability that the Yankees will lose a game is given as,
[tex]P(L)=1-P(W)\\\implies P(L)=1-0.53\\\implies P(L)=0.47[/tex]
It is also given that, the probability that the Yankees will score 5 or more runs is 0.48.
[tex]\implies P(A)=0.48[/tex] -----(1)
So, the probability that the Yankees will score less than 5 runs is,
[tex]P(S)=1-P(A)\\\implies P(S)=1-0.5\\\implies P(S)=0.5[/tex]------(2)
We also know the probability that the Yankees will win and score 5 or more runs is 0.42.
[tex]\implies P(B)=0.42[/tex]
Also, then the probability that the Yankees will lose or score less than 5 runs is given as,
[tex]P(C)=1-P(B)\\\implies P(C)=1-0.42\\\implies P(C)=0.58[/tex]
Next, the probability that the Yankees will lose and score less than 5 runs is,
[tex]P(D)=0.42+0.5-0.58\\\implies P(D)=0.34[/tex]
Now, the required probability is the probability that the Yankees will lose and score 5 or more runs.
It can be calculated using the conditional probability formula, [tex]P(M/N)=\frac{P(M\cap N)}{P(N)}[/tex]
So, the required probability that the Yankees will lose and score 5 or more runs is given as,
P(they score 5 or more runs / probability that they lose game) = P(they lose and score 5 or more runs) / P(they lose the game)
[tex]\implies P(E)=\frac{0.47-0.38}{0.47} \\\implies P(E)=0.2766[/tex]
Therefore, the probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.
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An object placed on a conveyor belt can move 9 feet every 18 seconds.
Plot two points that represent the distance an object would travel in different amounts of time at that rate.
Select two points on the coordinate grid. A line will connect the points.
Answers
A graph of the two (2) points (-0.5, 0) and (9, 0) that represent the distance which this object would travel in different amounts of time at that rate is shown in the image attached below.
How to write a linear function for the distance and time?Mathematically, a linear function is sometimes referred to as the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;
d = mt + b
Where:
d represents the distance.t represents the rate of change (slope).b represents the y-intercept.Therefore, the required linear function that relates the distance (d) and speed (s) at time (t) seconds is given by this mathematical expression;
d(t) = 18t + 9
For instance when time (t) = -0.5 seconds, the distance traveled by this object placed on a conveyor belt is given by;
d(t) = 18t + 9
d(-0.5) = 18(-0.5) + 9
d(-0.5) = -9 + 9
d(-0.5) = 0 feet.
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what times 7 equals 3.5
Answers
Answer:
Step-by-step explanation:
Answer 2
You would divide 7 by 3.5 and you get 2 If the equation was what times 3.5 =7
Factor the polynomial, 3x^2+x-10
Answers
[tex]3x^2+x-10=\boxed{(x+2)(3x-5)}[/tex]
From question 28 -29
Help please
Answers
g(x)=x-2/x+19 findg(-5)
Answers
Answer:
the functions domain is; x < -19 or x > -19
x= -19
Sorry otherwise im not sure what you need here :P
What is the RANGE of the cluster shown on this graph?
Answers
The range of the cluster shown in the graph is [1, 6]
What is range of a graph?
The range is all the values of the graph from down to up or on the x-axis.
Solution :
∵ Range is calculated from x-axis
∴ Range {1,2,3,4,5,6} = 6-1
= 5
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The range of the cluster shown in the graph is [1, 6]
What is range of a graph?The range is all the values of the graph from down to up or on the x-axis. The possible output values are displayed on the y-axis and make up the range. Remember that the domain and range of the graph could be larger than the visible values if it extends beyond the area that can be seen.
Solution :
∵ Range is calculated from x-axis
∴ Range {1,2,3,4,5,6} = 6-1
= 5
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367 Times 10 -3
Express the following numbers in scientific notation
Answers
Answer:
To express a number in scientific notation, you need to write it as a number between 1 and 10, multiplied by a power of 10.
In this case, 367 can be written as 3.67 x 100, and 10-3 can be written as 0.001.
Therefore, 367 x 10-3 can be expressed in scientific notation as:
3.67 x 0.001 = 0.00367
This can also be written as 3.67 x 10^-3. The ^ symbol indicates an exponent, and in this case, it means that the base number (3.67) is multiplied by 10 to the power of -3.
Step-by-step explanation:
Help me pls thank u
Answers
The value of slope for line equation 1 is -5/2. The value of slope for line equation 2 is 5/3.
What is slope?A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.
Here,
y=mx+c
where m is slope.
line equation 1,
y=-5/2x-5
m=-5/2
line equation 2,
y=5/3x
m=5/3
For line equation 1, the slope is equal to -5/2. For line equation 2, the slope is equal to 5/3.
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Please help me. Any answers help
Answers
Answer:
unexplainable
Step-by-step explanation:
does not make since
Find the missing length indicated.
Answers
Answer:
hope it help
the last answer is 6
I showed you step by step. for any explanation write it in the comment
Kiki painted 15 of her bookshelf on Monday and 56 of her bookshelf on Tuesday. She says she has painted 611 of her bookshelf.
Answers
what are we supposed to be solving
Answer:
Step-by-step explanation:
duh
Peter has collision insurance with $1000 deductible. He backs his car into a lamppost and causes $4300 worth of damage to the car. How much will his insurance company have to pay (assuming he is covered).
Answers
Since Peter has a $1000 deductible and the damages to the car are $4300, the insurance company will pay $4300 - $1000 = $3300 for the damages.
So, in this case, the insurance company will have to pay $3300 to cover the damages to Peter's car.
Someone please help me I’m dying hereThank you so muchhh!
Answers
By using the formula for area of rectangle, it can be calculated that-
a) Expression for total area = [tex]6^2 + 2 \times 6 + 24[/tex]
Total area = 72 square inches
b) Length of the figure = 9 inches
Breadth of the figure = 8 inches
What is area of a rectangle?
Area of a rectangle is the total space taken by the rectangle.
If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is calculated by
Area = l [tex]\times[/tex] b
Side of the square = 6 inches
Area of the square = [tex]6^2[/tex] square inches
Length of white rectangle = 2 inches
Breadth of white rectangle = 6 inches
Area of white rectangle = [tex]2 \times 6 =[/tex] 12 square inches
Area of blue rectangle = 24 square inches
Total area = [tex]6^2 + 2 \times 6 + 24[/tex] =
36 + 12 + 24 =
72 sq. inches
b) Let the breadth of the blue rectangle be b inches
Length of the blue rectangle = 2 + 6 = 8 inches
Total area = 8b square inches
By the problem,
[tex]8b = 24 \\b = \frac{24}{8}\\[/tex]
b = 3 inches
Length of the figure = 6 + 3 = 9 inches
Breadth of the figure = 2 + 6 = 8 inches
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Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution. u = x 4(x +1) x +1 (x + 1)2 Select the solution(s) of the original equation. x = 1 +
Answers
The solutions for the given equation are x=-3 and x=1.
The given equation is (x + 1)² - 4(x + 1) + 2 = 0.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
(x + 1)² - 4(x + 1) + 2 = 0
⇒ (x + 1)² - 4(x + 1)=-2
⇒ (x+1)[(x+1)-4]=-2
⇒ x+1=-2, (x+1)-4=-2
⇒ x=-2-1, x+1=-2+4
⇒ x=-3, x+1=2
⇒ x=-3, x=1
Therefore, the solutions for the given equation are x=-3 and x=1.
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Work out the volume of this half-cylinder.
Give your answer in terms of π.
The diagram is not drawn to scale.
Answers
Answer:
Vhc = 401.92 cm3
Step-by-step explanation:
Vcylender = Pi*r2*h
Vhalfcyldr = (Pi*r2*h)/2
then
h= 16cm
r = 8cm/2 = 4cm
then
Vhalfcylinder = ((3.14)*(4)2*16) / 2
Vhc = 401.92 cm3
Question Solve 6=t/5
Answers
Answer:
30=t i think
Step-by-step explanation:
So basically what you do is since it is division you would multiply 5 by its self and you multiply on the other side because if you do something on one side you have to do it on another so that would leave you with 30=t
Multiply 5 to both sides
30=t
Swap side
T=30
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An employee who earns $12/hour, worked 37 hours this week, is paid a commission of $40 for each sale, and makes 9 sales during the same week, has earned total commissions of $ .
Answers
The total commission that's earned will be $360.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, an employee who earns $12/hour, worked 37 hours this week, is paid a commission of $40 for each sale, and makes 9 sales during the same week. Employees receive commission, also referred to as a sales commission, based on the sales they generate. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services. Sales commissions are a common incentive used by employers to boost employee productivity. A commission can be paid instead of or in addition to a salary.
The total commissions will be:
= Amount of commission × Number of sales
= $40 × 9
= $360
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The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A = 120 − 2x ∠B = 70 + x ∠C = 105 − x2 ∠D = 40 + 4x
Answers
The value of x from the parallelogram ABCD is 10.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
Given that, ∠A=120-2x, ∠B=70+x, ∠C=105-x² and ∠D=40+4x.
The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary.
Here, ∠A and ∠D are consecutive angles
Now, 120-2x+40+4x=180
⇒ 160+2x=180
⇒ 2x=20
⇒ x=10
So, ∠A=120-2x=100, ∠B=70+x=80, ∠C=160-6x=100 and ∠D=40+4x=80
Therefore, the value of x is 10.
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"Your question is incomplete, probably the complete question/missing part is:"
The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A=120-2x, ∠B=70+x, ∠C=160-6x and ∠D=40+4x.
Determine a series of transformations that would map polygon ABCD onto poly
A'B'C'D'?
Answers
The polygon ABCD is transformed 4 units to the left after being reflected across the x-axis.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
Reflect the polygon ABCD across the x-axis as;
A(x, y) → A'(x, -y) (x, -y) (x, -y)
According to this rule, A's coordinates are
A(1, -5) → A'(1, 5) (1, 5) (1, 5)
ABCD is shifted 4 units further to the left.
Now apply to the translation:
A"(x - 4, y) = A'(x, y) (x - 4, y)
A'(1, 5) → A"(1 - 4, 5) (1 - 4, 5) (1 - 4, 5)
→ A"(-3, 5) (-3, 5) (-3, 5)
Thus Polygon ABCD will eventually overlap Polygon A'B'C'D' through a series of transformations.
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Enter the equation of the circle described below.
Center (0, 8), radius = 8
x2 + (y -
)2 =
Answers
The equation of the circle described in the problem is x² + (y - 8)² = 64.
What is the equation of a circle?
The general equation of any type of circle is represented by: x2 + y2 + 2gx + 2fy + c = 0, for all values of g, f, and c.
The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.
The standard form equation of a circle with center at (h, k) and radius r is given by:
(x - h)² + (y - k)² = r²
Substituting the given values into this equation, we get:
(x - 0)² + (y - 8)² = (8)²
Simplifying this equation gives:
x² + (y - 8)² = 64
Hence, This is the equation of the circle described in the problem.
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Select the expression that represents the ADDITION of
the two number lines.
O-10x+ 5x - 30x
O-10x-5x + 30x
O 10x + 5x - 30x
Answers
An expression that represents the ADDITION of the two number lines is: B. -10x - 5x + 30x.
Each segment equals 5x and the first arrow is 30x long.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Based on the number line shown above, we can reasonably infer and logically deduce that each of its segment is equal to 5x with the longest arrow measuring 30x on the number line.
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I AM ON A TEST HELP WHAT IS THE MAXIMUM OR MINIMUM VALUE AND WHAT ARE THE COORDINATES OF THE VERTEX y=2x^2+12x+5
Answers
The parabola's vertex is (-3/2, -22). Because this is the lowest point on the parabola, the function's minimum value is -22.
To determine the maximum or minimum value of the quadratic function y = 2x² + 12x + 5, you need to find the vertex of the parabola formed by this function.
To find the vertex of the parabola, you can use the formula x = -b / (2a), where x is the x-coordinate of the vertex, a is the coefficient of the x² term, and b is the coefficient of the x term.
In this case, the coefficient of the x² term is 2, and the coefficient of the x term is 12. Therefore, the x-coordinate of the vertex is x = -12 / (2×2) = -6 / 4 = -3/2.
To find the y-coordinate of the vertex, you can substitute the x-coordinate back into the original equation:
y = 2(-3/2)² + 12(-3/2) + 5 = 2(-9/4) + (-18) + 5 = -9 + (-18) + 5 = -22.
Therefore, the vertex of the parabola is (-3/2, -22). This is the lowest point on the parabola, so the minimum value of the function is -22.
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